The theatre opened in 1963 and was named after its founder, Jeannetta Cochrane, who was a theatre practitioner specialising in costume and scenery design at the Central School of Art and Design, now part of the University of the Arts London.

Through her persistence, Cochrane persuaded the London County Council to build a theatre attached to the school that could be used as a practice space.

[3] In June 2015 Channel 4 filmed a TFI Friday special at the theatre and a series of ten shows were produced live in October through December 2015.

Cochrane Theatre was chosen for the new series as the original location of Riverside Studios where the show was filmed has been demolished and is being redeveloped, due for completion in autumn 2017.

Channel 5's Do the Right Thing with Eamonn Holmes and Ruth Langsford was filmed at the Cochrane Theatre in 2019.